Abstract
We study linear stability of viscous flows in a squeezelubrication film, in which the flow varies slowly in space and time,between two parallel plates moving normal to each other with a slowconstant speed, generalizing the inviscid results of Aristov and Gitman[J. Fluid Mech. 464 (2002) 209]. The temporalevolution of two-dimensional disturbances for this physical situation,including the asymptotic behaviour of a long term or the transientbehaviour of some time interval, is obtained by the construction of alow-dimensional Galerkin method. It is found that the wall boundariestypically play dual roles of stabilizer and destabilizer. Theyconstrain the development of disturbances and have stabilizinginfluences. However, they give rise to velocity shear, which isdiffused by viscosity and thereby tends to destabilize the flow.
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